While it was already known to A. Hurwitz in 1893 that the automorphism group of a complex curve of general type acts faithfully on the (singular) cohomology of the curve, there is still no satisfying answer for the corresponding question in the case of smooth and projective algebraic surfaces, even over the complex numbers. The first examples of surfaces for which the action of the automorphism group on cohomology is not faithful, even though the group is discrete, were Enriques surfaces.In 1984, S. Mukai and Y. Namikawa obtained a complete classification of complex Enriques surfaces with such numerically trivial automorphisms. I will explain how to obtain the classification of the possible numerically trivial automorphism groups of Enriques surfaces in arbitrary positive characteristic.